Which element of group 15 shows $+3$ as its predominant oxidation state, being much more stable than $+5$?

Down group 15 the inert pair effect strengthens, so the $+3$ state grows more stable relative to $+5$. Bismuth is the extreme case: Bi(III) compounds are stable, while Bi(V) compounds such as $\mathrm{NaBiO}{}_3$ are strongly oxidising.